By D. Iesan
Reflecting new advancements within the examine of Saint-Venant’s challenge, Classical and Generalized versions of Elastic Rods makes a speciality of the deformation of elastic cylinders for 3 versions of continuum: classical elastic continuum, Cosserat elastic physique, and porous elastic fabric.
The writer offers a style to build Saint-Venant’s ideas, minimal power characterizations of those recommendations, and an evidence of Saint-Venant’s precept. He then discusses the deformation of nonhomogenous and isotropic cylinders in addition to the matter of loaded anisotropic elastic cylinders. The ebook additionally bargains with the deformation of cylinders in the linearized thought of homogeneous Cosserat elastic solids, the deformation of nonhomogeneous Cosserat cylinders, and the extension, bending, and torsion of porous elastic cylinders.
With various effects no longer present in similar texts, this ebook offers a distinct, unified viewpoint within the thought of the deformation of elastic cylinders.
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Extra info for Classical and generalized models of elastic rods
The ﬁrst precise general treatment of any version of Saint-Venant’s principle was that of Sternberg , who formulated and proved the version suggested by Mises. Two alternative versions of Saint-Venant’s principle were established by Toupin  and Knowles . These authors arrived at estimates for the strain energy Uz contained in that portion of the body which lies beyond a distance z from the load region. The idea of using Uz in the formulation of Saint-Venant’s principle is due to Zanaboni [343,344].
In what follows we assume that the functions uα and tαβ are single-valued. 461 we see that the real part of Ω is single-valued, but, in describing once each interior contour Γk , the imaginary part of Ω acquires a constant increment denoted by 2πAk . 2 A multiply-connected domain. 57) k=1 where zk is a point in the simply-connected region Sk , bounded by Γk , is single-valued and analytic in Σ1 . 58) k=1 where γk are complex constants, and Ω0 is an analytic and single-valued function on Σ1 . 46 are single-valued, it follows that ω is also single-valued on Σ1 .
This result is due to M. L´evi (1898). 16 hold. We now establish a representation of the displacements in terms of a pair of complex analytic functions of the complex variable z = x1 + ix2 . The boundary-value problems can be reduced to the determination of these functions from prescribed values of certain combinations of these functions on the boundary of Σ1 . 36) where a bar over a letter designates the complex conjugate. 40) where Ω is an arbitrary analytic complex function on z, and Ω (z) = dΩ(z)/dz.
Classical and generalized models of elastic rods by D. Iesan